
The field operators \(\psi _\uparrow ({\mathbf {r}})\)  and \(\psi _\downarrow ^\dagger ({\mathbf {r}})\) 
contain the rapid oscillation term \({\rm e}^{{\rm i}{\mathbf {k}_{\rm F}}\cdot {\mathbf {r}}}\) ,
while the field operators \(\psi _{{\mathbf {k}_{\rm F}}\uparrow }({\mathbf {r}})\)  and \(\psi _{-{\mathbf {k}_{\rm F}}\downarrow }^\dagger ({\mathbf {r}})\)  describe
slowly varying component of the order of the superconducting coherence length.
We substitute Eq. (REF ) into Eq. (REF ) and apply the quasi-classical approximation,
[1]}, [2]}
where the relative coordinate \({\mathbf {x}}={\mathbf {r}}-{\mathbf {r}}^{\prime }\)  and the center of mass coordinate \({\mathbf {R}}=({\mathbf {r}}+{\mathbf {r}}^{\prime })/2\)  are introduced.
The two coordinates, \({\mathbf {r}}\)  and \({\mathbf {r}}^{\prime }\) , are then expressed as \({\mathbf {r}}={\mathbf {R}}+{\mathbf {x}}/2\)  and \({\mathbf {r}}^{\prime }={\mathbf {R}}-{\mathbf {x}}/2\) .
The order parameter is written by \({\mathbf {x}}\)  and \({\mathbf {R}}\)  as
\(\Delta ({\mathbf {r}},{\mathbf {r}}^{\prime }) \rightarrow \Delta ({\mathbf {x}},{\mathbf {R}}).\) 
